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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · MultivariateStats.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>MultivariateStats.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="whiten/">Data Transformation</a></li><li><a class="tocitem" href="lreg/">Regression</a></li><li><a class="tocitem" href="lda/">Linear Discriminant Analysis</a></li><li><a class="tocitem" href="pca/">Principal Component Analysis</a></li><li><a class="tocitem" href="ica/">Independent Component Analysis</a></li><li><a class="tocitem" href="cca/">Canonical Correlation Analysis</a></li><li><a class="tocitem" href="fa/">Factor Analysis</a></li><li><a class="tocitem" href="mds/">Multidimensional Scaling</a></li><li><a class="tocitem" href="api/">Development</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/MultivariateStats.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="MultivariateStats.jl-Documentation"><a class="docs-heading-anchor" href="#MultivariateStats.jl-Documentation">MultivariateStats.jl Documentation</a><a id="MultivariateStats.jl-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#MultivariateStats.jl-Documentation" title="Permalink"></a></h1><p><a href="https://github.com/JuliaStats/MultivariateStats.jl">MultivariateStats.jl</a> is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.</p><ul><li><a href="whiten/#Data-Transformation">Data Transformation</a></li><li class="no-marker"><ul><li><a href="whiten/#Whitening">Whitening</a></li></ul></li><li><a href="lreg/#Regression">Regression</a></li><li class="no-marker"><ul><li><a href="lreg/#Examples">Examples</a></li><li><a href="lreg/#Linear-Least-Square">Linear Least Square</a></li><li><a href="lreg/#Ridge-Regression">Ridge Regression</a></li><li><a href="lreg/#Isotonic-Regression">Isotonic Regression</a></li></ul></li><li><a href="lda/#Linear-Discriminant-Analysis">Linear Discriminant Analysis</a></li><li class="no-marker"><ul><li><a href="lda/#Example">Example</a></li><li><a href="lda/#Two-class-Linear-Discriminant-Analysis">Two-class Linear Discriminant Analysis</a></li><li><a href="lda/#Multi-class-Linear-Discriminant-Analysis">Multi-class Linear Discriminant Analysis</a></li><li><a href="lda/#Subspace-Linear-Discriminant-Analysis">Subspace Linear Discriminant Analysis</a></li></ul></li><li><a href="pca/#Principal-Component-Analysis">Principal Component Analysis</a></li><li class="no-marker"><ul><li><a href="pca/#Example">Example</a></li><li><a href="pca/#Linear-Principal-Component-Analysis">Linear Principal Component Analysis</a></li><li><a href="pca/#Kernel-Principal-Component-Analysis">Kernel Principal Component Analysis</a></li><li><a href="pca/#Probabilistic-Principal-Component-Analysis">Probabilistic Principal Component Analysis</a></li></ul></li><li><a href="ica/#Independent-Component-Analysis">Independent Component Analysis</a></li><li class="no-marker"><ul><li><a href="ica/#FastICA">FastICA</a></li></ul></li><li><a href="cca/#Canonical-Correlation-Analysis">Canonical Correlation Analysis</a></li><li><a href="fa/#Factor-Analysis">Factor Analysis</a></li><li><a href="mds/#Multidimensional-Scaling">Multidimensional Scaling</a></li><li class="no-marker"><ul><li><a href="mds/#Example">Example</a></li><li><a href="mds/#Classical-Multidimensional-Scaling">Classical Multidimensional Scaling</a></li><li><a href="mds/#Metric-Multidimensional-Scaling">Metric Multidimensional Scaling</a></li></ul></li><li><a href="api/#API-Reference">API Reference</a></li><li class="no-marker"><ul><li><a href="api/#Current">Current</a></li><li><a href="api/#New">New</a></li></ul></li></ul><p><strong>Notes:</strong> All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="whiten/">Data Transformation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Tuesday 2 May 2023 21:06">Tuesday 2 May 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · MultivariateStats.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>MultivariateStats.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="whiten/">Data Transformation</a></li><li><a class="tocitem" href="lreg/">Regression</a></li><li><a class="tocitem" href="lda/">Linear Discriminant Analysis</a></li><li><a class="tocitem" href="pca/">Principal Component Analysis</a></li><li><a class="tocitem" href="ica/">Independent Component Analysis</a></li><li><a class="tocitem" href="cca/">Canonical Correlation Analysis</a></li><li><a class="tocitem" href="fa/">Factor Analysis</a></li><li><a class="tocitem" href="mds/">Multidimensional Scaling</a></li><li><a class="tocitem" href="api/">Development</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/MultivariateStats.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="MultivariateStats.jl-Documentation"><a class="docs-heading-anchor" href="#MultivariateStats.jl-Documentation">MultivariateStats.jl Documentation</a><a id="MultivariateStats.jl-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#MultivariateStats.jl-Documentation" title="Permalink"></a></h1><p><a href="https://github.com/JuliaStats/MultivariateStats.jl">MultivariateStats.jl</a> is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.</p><ul><li><a href="whiten/#Data-Transformation">Data Transformation</a></li><li class="no-marker"><ul><li><a href="whiten/#Whitening">Whitening</a></li></ul></li><li><a href="lreg/#Regression">Regression</a></li><li class="no-marker"><ul><li><a href="lreg/#Examples">Examples</a></li><li><a href="lreg/#Linear-Least-Square">Linear Least Square</a></li><li><a href="lreg/#Ridge-Regression">Ridge Regression</a></li><li><a href="lreg/#Isotonic-Regression">Isotonic Regression</a></li></ul></li><li><a href="lda/#Linear-Discriminant-Analysis">Linear Discriminant Analysis</a></li><li class="no-marker"><ul><li><a href="lda/#Example">Example</a></li><li><a href="lda/#Two-class-Linear-Discriminant-Analysis">Two-class Linear Discriminant Analysis</a></li><li><a href="lda/#Multi-class-Linear-Discriminant-Analysis">Multi-class Linear Discriminant Analysis</a></li><li><a href="lda/#Subspace-Linear-Discriminant-Analysis">Subspace Linear Discriminant Analysis</a></li></ul></li><li><a href="pca/#Principal-Component-Analysis">Principal Component Analysis</a></li><li class="no-marker"><ul><li><a href="pca/#Example">Example</a></li><li><a href="pca/#Linear-Principal-Component-Analysis">Linear Principal Component Analysis</a></li><li><a href="pca/#Kernel-Principal-Component-Analysis">Kernel Principal Component Analysis</a></li><li><a href="pca/#Probabilistic-Principal-Component-Analysis">Probabilistic Principal Component Analysis</a></li></ul></li><li><a href="ica/#Independent-Component-Analysis">Independent Component Analysis</a></li><li class="no-marker"><ul><li><a href="ica/#FastICA">FastICA</a></li></ul></li><li><a href="cca/#Canonical-Correlation-Analysis">Canonical Correlation Analysis</a></li><li><a href="fa/#Factor-Analysis">Factor Analysis</a></li><li><a href="mds/#Multidimensional-Scaling">Multidimensional Scaling</a></li><li class="no-marker"><ul><li><a href="mds/#Example">Example</a></li><li><a href="mds/#Classical-Multidimensional-Scaling">Classical Multidimensional Scaling</a></li><li><a href="mds/#Metric-Multidimensional-Scaling">Metric Multidimensional Scaling</a></li></ul></li><li><a href="api/#API-Reference">API Reference</a></li><li class="no-marker"><ul><li><a href="api/#Current">Current</a></li><li><a href="api/#New">New</a></li></ul></li></ul><p><strong>Notes:</strong> All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="whiten/">Data Transformation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 1 April 2024 05:46">Monday 1 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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